The present invention relates to transmission diversity. More particularly, the present invention relates to mitigating intersymbol interference in systems which employ delay transmit diversity.
In radio transmissions, a transmitted signal may be deflected off buildings or other obstacles between a transmitter and a receiver. The deflection may cause a receiver to receive multiple versions of the transmitted signals with different time delays. The reception of a transmitted signal which is deflected off objects and the reception of multiple time delayed versions of the transmitted signal is known as multipath propagation. In digital transmissions, if the delay between the multiple paths exceeds the symbol duration, signal distortion known as intersymbol interference (ISI) is generated. Various transmission schemes are designed to mitigate ISI. One type of transmission scheme which is particularly suited for mitigating ISI is known as orthogonal frequency division multiplexing (OFDM). OFDM divides a bandwidth into a number of small subcarriers. Through the use of orthogonal functions, the spectrum of all subscarriers can mutually overlap, thus yielding optimum bandwidth efficiency. However, when the delay difference between multiple paths exceeds the minimum sampling interval the orthogonality between subcarriers is destroyed. To maintain the condition of perfect orthogonality between subcarriers in a multipath environment, a guard interval, or cyclic prefix (CP), is inserted before the transmission of each symbol.
FIG. 1 illustrates a conventional transmitter and receiver which operate according to OFDM. The transmitter takes a symbol S(k) and performs an inverse fast Fourier transform (IFFT) to convert the symbol to be transmitted from the frequency domain into the time domain. The transmitter also adds a cyclic prefix (CP) to the symbol to be transmitted. The time domain symbol s(n) is transmitted via antenna Ant 1TX over a transmission medium, e.g., an air interface, to a receiver. The transmission medium convolves the transmitted symbol with the channel impulse response h1. The transmitted symbol is received via antenna Ant 1TX. The symbol as received by the receiver can be represented in the time domain by s(n)*h1(n). The receiver then removes the cyclic prefix and performs a fast Fourier transform (FFT). The received symbol in the frequency domain can be represented by S(k)H1(k), wherein S(k) is the received symbol in the frequency domain and H1(k) is the frequency representation of the channel, known as the channel transfer function.
FIG. 2 illustrates a conventional OFDM symbol M and associated cyclic prefix. OFDM symbol M, as represented in the time domain, contains sample points 1 through N. The cyclic prefix that is associated with OFDM symbol M contains sample points N−2 through N of OFDM symbol M. Since multipath delays can destroy the orthogonality of the transmitted symbol, the cyclic prefix is set to a number of sample points which is longer than the worst case multipath delay between the transmitter and the receiver. Accordingly, one skilled in the art will recognize that although the cyclic prefix illustrated in FIG. 2 contains only three sample points, N−2 through N, the number of actual sample points in a cyclic prefix will vary depending upon the worst case multipath delay.
Typically, transmitted signals in different frequencies are affected differently by the transmission medium. However, transmitted signals in different frequencies may be subject to flat Rayleigh fading, i.e., fading which occurs across the whole frequency domain. Further, when the delay difference between multiple paths is significantly shorter than a sample point duration the phase of the signals in the multiple paths may either add up in phase constructively or may cancel each other out. When the phase of the signals in the multiple paths cancel each other out, the quality of the received signal depends upon whether one strong direct signal is received or whether scattered signals from many directions with random phase are received. When multiple scattered signals from many directions with random phase are received with a delay spread significantly smaller than the sample point duration, flat Rayleigh fading is caused in the frequency domain. For example, a receiver may not be able to recover any of the subcarriers associated with a transmitted OFDM symbol which experiences flat Rayleigh fading. When the transmitted OFDM symbol is subject to flat Rayleigh fading, the quality of service (QOS) will be severely degraded. One method for providing a better quality of service in a flat Rayleigh fading environment is to use transmission diversity.
FIG. 3 illustrates a conventional transmitter and receiver which operate according to OFDM, wherein the transmitter transmits using transmission diversity. As illustrated in FIG. 3, transmission diversity is provided by employing a set of M of transmit antennas each of which transmit delayed versions of a symbol to be transmitted. One skilled in the art will recognize that transmission diversity is sometimes employed in a CDMA system, wherein independent delayed paths are resolved and then combined using, e.g., maximum ratio combining. When employing transmission diversity in an OFDM system, the transmit antennas should be positioned such that statistical independent channels are seen by the receiver. In other words, the transmitted symbol will be subject to individually independent flat Rayleigh fading channels. Employing a transmission diversity scheme, such as the one illustrated in FIG. 3, creates a coverage area where individual terminals experience a relatively uniform total received power without regard to position and time. Further, the transmission diversity scheme illustrated in FIG. 3 also creates pseudorandom frequency selectivity in the channel which also provides a more uniform receiving condition provided some type of coding is employed, i.e., forward error correction coding (FEC). One skilled in the art will recognize that word error rates, or OFDM symbol error rates, are lower for a FEC coded message in a fast uncorrelated Rayleigh fading channel than in a slow correlated Rayleigh fading channel. Accordingly, the delay based transmission diversity scheme illustrated in FIG. 3, is intended to introduce such uncorrelated frequency selectivity.
As illustrated in FIG. 3, the transmitter initially performs an inverse fast Fourier transform and then adds a cyclic prefix to a frequency domain symbol to be transmitted S(k). The inverse fast Fourier transform converts the frequency domain symbol S(k) into a time domain symbol s(n). The time domain symbol s(n) is sent along separate paths associated with each of the antennas. The time domain symbol s(n) passes through attenuators, Atten1 through AttenM, which attenuates the power of the transmitted symbol in each antenna path by the square root of the number of antennas used in the transmission diversity scheme to normalize the overall transmitted power. Other than in the first antenna path, the attenuated time domain symbol to be transmitted is then subject to a linear delay. The linear delay in each path can be represented by the following formula:p*(T/N) for p from 0 to M−1                 where p is in the range of 0 to M−1wherein p is an index to the antenna under consideration, M represents the total number of antennas in the diversity system, T represents the time duration of the OFDM symbol without a cyclic prefix, and N represents the number of subcarriers present in the frequency domain. The symbols transmitted from antennas Ant 1TX through Ant MTX are respectively subjected to channel transfer functions H1 through HM of the transmission medium. At the receiver the symbols from the antennas Ant 1TX through Ant MRX are received by antenna Ant 1RX and combined together. As illustrated in FIG. 3, after being combined in the receiver, the resultant symbol can be represented in the time domain by s(n)*(h1(n)+h2(n)+. hM(n)). The receiver then removes the cyclic prefix and performs a fast Fourier transform to convert the time domain symbol into a frequency domain symbol.        
FIG. 4 illustrates in more detail three symbols respectively transmitted from three antennas with different delays. At the receiver a fast Fourier transform is performed during a set period of time known as a fast Fourier transform window. As illustrated in FIG. 4, by using a cyclic prefix the fast Fourier transform window is performed over all the sample points of the transmitted OFDM symbol n of each of the delayed versions of the transmitted symbols.
In the frequency domain, the received symbol can be represented by:       R    ⁢                   ⁢          (      k      )        =                              S          ⁢                                           ⁢                      (            k            )                                    M                    ·                        ∑                      i            =            1                    M                ⁢                                   ⁢                              H            1                    ⁢                                           ⁢                      (            k            )                                =          S      ⁢                           ⁢                        (          k          )                ·        H            ⁢                           ⁢              (        k        )            wherein S(k) is the sent symbol, M is the number of antennas and H(k) is the composite frequency response of the channel where the square root factor of M is included. Thus, the standard deviation of H(k) remains constant.
The received power according to Parsevals (DFT) theorem is:   P  =                    1        N            ⁢                           ⁢                        ∑                      k            =            0                                N            -            1                          ⁢                                   ⁢                  R          ⁢                                           ⁢                                    (              k              )                        ·            R                    ⁢                                           ⁢                                    (              k              )                        *                                =                  1        N            ⁢                           ⁢                        ∑                      k            =            0                                N            -            1                          ⁢                                   ⁢                                                                          h                ⁢                                                                   ⁢                                  (                  k                  )                                                                    2                    ⁢                                                                  S                ⁢                                                                   ⁢                                  (                  k                  )                                                                    2                              
where R(k) is a frequency domain representation of the received symbol and R(k)* is the complex conjugate of R(k). Assuming that S(k) uses multilevel constellations, e.g., 16 QAM or 64 QAM, for each k, the average power level per subcarrier is:   P  =            E      ⁢                           ⁢              (                              1            N                    ⁢                                           ⁢                                    ∑                              k                =                0                                            N                -                1                                      ⁢                                                   ⁢                                                                                                  H                    ⁢                                                                                   ⁢                                          (                      k                      )                                                                                        2                            ⁢                                                                                      S                    ⁢                                                                                   ⁢                                          (                      k                      )                                                                                        2                                                    )              =                            σ          s          2                N            ⁢                           ⁢                        ∑                      k            =            0                                N            -            1                          ⁢                                   ⁢                                                        H              ⁢                                                           ⁢                              (                k                )                                                          2                    wherein E represents the expected value.
If it is assumed that transmission diversity system employs two antennas, wherein each antenna transmits over a path which is affected by a complex Gaussian attenuation variable Hi, i.e., a flat Rayleigh fading channel, and that the second diversity path is delayed by, e.g., one OFDM sampling point, the resulting transfer function then becomes:       H    ⁢                   ⁢          (      k      )        =            H      0        +                  H        1            ·              ⅇ                  -                                    j              ⁢                                                           ⁢              2              ⁢                                                           ⁢                              π                ·                k                                      N                              
Solving now for the received power results in the following:                     P        =                ⁢                                                            σ                s                2                            N                        ⁢                                                   ⁢                                          ∑                                  k                  =                  0                                                  N                  -                  1                                            ⁢                                                           ⁢                                                                                      H                    0                                                                    2                                              +                                                                  H                1                                                    2                    +                                    2              ·                                                                H                  0                                                            ·                                                                H                  1                                                                      ⁢                                                   ⁢            cos            ⁢                                                   ⁢                          (                                                arg                  ⁢                                                                           ⁢                                      (                                          H                      0                                        )                                                  -                                  arg                  ⁢                                                                           ⁢                                      (                                          H                      1                                        )                                                              )                                                              =                ⁢                                            σ              s              2                        N                    ⁢                                           ⁢                      (                                          N                ·                                                                                                H                      0                                                                            2                                            +                              N                ·                                                                                                H                      1                                                                            2                                            +                              2                ·                                                                        H                    0                                                                    ·                                                                        H                    1                                                                    ·                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                                           ⁢                                      cos                    ⁢                                                                                   ⁢                                          (                                                                                                    -                            2                                                    ·                          π                          ·                          k                                                N                                            )                                                                                            )                                                  =                ⁢                              σ            s            2                    ⁢                                           ⁢                      (                                                                                                  H                    0                                                                    2                            +                                                                                      H                    1                                                                    2                                      )                                                  =                ⁢                              σ            s            2                    ⁢                                           ⁢                      (                                          H                re0                2                            +                              H                tm0                2                            +                              H                re1                2                            +                              H                tm1                2                                      )                              
where Hre represents the real portion of the complex valued H and Him represents the imaginary portion of the complex valued H.
As seen above, the received power is a centrally distributed chi-square variable of degree four. If, however, there was no delay between the two transmitted symbols H0 and H1, the symbols can be merged together as H′ before power summation over all subcarriers. The net result is then a chi-square variable of degree two, i.e., Rayleigh distributed. Although the example given above relates to a system employing two antennas, one skilled in the art will recognize that the degree n of the chi-square variable is equal to two times the number of antennas with different delays, i.e., n=2M.
The average value and standard deviation of a chi-square variable is:E(P)=nσ2, and σp=√{square root over (2n)}·σ2, where σ is the standard deviation of each Gaussian distributed variable that compose the chi-square distributed variable.
It should be noted that the relative spread, i.e., the stochastic deviation around the mean value of the power P, is reduced when the degree n is increased as:σP/E(P)=√{square root over (2/n)}
FIG. 5 illustrates the power carrier distribution function (CDF) for M=2 antennas. Curve 505 illustrates the power carrier distribution function for two antennas with different delays, while curve 510 illustrates power carrier distribution function for transmission on two antennas with no delay. As can be seen from FIG. 5, using different delays for each antenna results in a steeper carrier distribution function curve. It will be recognized that carrier distribution function which is a vertical line indicates that there are no variations around the mean value, and hence, the symbol is deterministic, i.e., non-random. Accordingly, a steeper curve indicates that the overall power level is more deterministic.
FIG. 6 illustrates the subcarrier covariance matrix for transmission over six antennas without any delay of the symbol transmitted over the six antennas. As can be seen from FIG. 6, each subcarrier channel is correlated with all the other subcarrier channels when the antennas transmit the same symbol without a delay difference between the antennas. If the transmission channel subjects the transmitted symbol to a flat Rayleigh fading, the transmitted symbol of the six antennas will be similarly affected by the channel transfer function.
FIG. 7 illustrates the subcarrier covariance matrix for the transmission of a symbol over six antennas with six different delays assuming a flat Rayleigh fading channel. As can be seen from FIG. 7, the subcarriers have a low value of correlation, i.e., most subcarriers have an absolute correlation value of less than 0.2. Accordingly, if the transmission medium subjected the symbols transmitted by the six antennas to a flat Rayleigh channel, most subcarriers would be affected differently by the channel.
Although the transmission of OFDM symbols using a plurality of antennas each with a different delay helps prevent the symbol being transmitted from being corrupted by flat Rayleigh fading, the total delay spread between all of the antenna paths can be no more than the duration of the cyclic prefix minus the duration of the inherent channel delay spread. It will be recognized that the delay spread is a measure of how distributed the different delays are with respect to each other. Introducing a greater delay would result in intersymbol interference, and subsequently the subcarriers would lose their mutual orthogonality. Accordingly, since the longer the cyclic prefix the less usable bandwidth is available for transmission of data, cyclic prefixes are typically kept as short as possible.
Accordingly, it would be desirable to provide a transmission diversity scheme using OFDM which is not limited by the duration of the cyclic prefix minus the duration of the inherent channel delay spread.